\contentsline {section}{\tocsection {}{1}{Introduction}}{2}
\contentsline {subsection}{\tocsubsection {}{1.1}{Installation instructions}}{2}
\contentsline {section}{\tocsection {}{2}{Basic functions}}{3}
\contentsline {subsection}{\tocsubsection {}{2.1}{Finite $q$-products}}{3}
\contentsline {subsubsection}{\tocsubsubsection {}{2.1.1}{Rising $q$-factorial}}{3}
\contentsline {subsubsection}{\tocsubsubsection {}{2.1.2}{Gaussian polynomials}}{3}
\contentsline {subsection}{\tocsubsection {}{2.2}{Infinite products}}{3}
\contentsline {subsubsection}{\tocsubsubsection {}{2.2.1}{Dedekind eta products}}{3}
\contentsline {subsubsection}{\tocsubsubsection {}{2.2.2}{Theta functions}}{4}
\contentsline {section}{\tocsection {}{3}{Product Conversion}}{5}
\contentsline {subsection}{\tocsubsection {}{3.1}{{\tt prodmake}}}{5}
\contentsline {subsection}{\tocsubsection {}{3.2}{{\tt qfactor}}}{6}
\contentsline {subsection}{\tocsubsection {}{3.3}{{\tt etamake}}}{8}
\contentsline {subsection}{\tocsubsection {}{3.4}{{\tt jacprodmake}}}{10}
\contentsline {section}{\tocsection {}{4}{The Search for Relations}}{12}
\contentsline {subsection}{\tocsubsection {}{4.1}{{\tt findhom}}}{12}
\contentsline {subsection}{\tocsubsection {}{4.2}{{\tt findhomcombo}}}{13}
\contentsline {subsection}{\tocsubsection {}{4.3}{{\tt findnonhom}}}{15}
\contentsline {subsection}{\tocsubsection {}{4.4}{{\tt findnonhomcombo}}}{16}
\contentsline {subsection}{\tocsubsection {}{4.5}{{\tt findpoly}}}{17}
\contentsline {section}{\tocsection {}{5}{Sifting coefficients}}{19}
\contentsline {section}{\tocsection {}{6}{Product Identities}}{20}
\contentsline {subsection}{\tocsubsection {}{6.1}{The Triple Product Identity}}{20}
\contentsline {subsection}{\tocsubsection {}{6.2}{The Quintuple Product Identity}}{21}
\contentsline {subsection}{\tocsubsection {}{6.3}{Winquist's Identity}}{23}
\contentsline {section}{\tocsection {}{}{References}}{25}